Okay, so I need to figure out the correct chemical formula for this di-substituted 6-membered aromatic ring compound. Let me start by analyzing the given information step by step.

First, the compound is a di-substituted aromatic ring, which typically means it has two substituents attached to the benzene ring. The FTIR spectrum shows an ester group. Esters have a carbonyl group (C=O) and an oxygen atom, so that's likely part of the substituents on the ring.

The 1H NMR spectrum has six signals. Let's break those down:

1. Two aromatic-H signals. Since it's a di-substituted benzene ring, there could be two sets of equivalent protons. For example, if the substituents are para to each other, there would be two types of aromatic protons. But wait, if it's a di-substituted ring, the substituents could be in positions that create symmetry. However, the NMR shows two signals for aromatic-H, which suggests that there are two distinct sets of aromatic protons. Maybe the molecule has a para-substituted group and another substituent in a position that breaks symmetry, leading to two different aromatic environments. Or perhaps it's a meta substitution with another substituent. Hmm.

2. Two signals for vinyl-H: one is a doublet, and the other is a doublet of quartets. Vinyl protons (like those in a vinyl group or attached to a double bond) typically show up as multiplets. The fact that there's a doublet and a doublet of quartets suggests that one of the vinyl protons is coupling with one neighboring proton (doublet), and the other is coupling with two protons (quartet). Wait, but vinyl groups usually have two protons. For example, in a structure like CH2=CH-O-R, the two protons on the CH2 would be split into a doublet of quartets if each is adjacent to a CH group. Alternatively, maybe the protons are in a conjugated system where one is next to a substituent and the other is in a different environment.

3. Two signals for –CH3 groups. Since there are no –CH2 groups indicated by the NMR (no signals for CH2), the methyl groups must be attached directly to the ring or in a way that doesn't produce a CH2 group in the NMR. Methyl groups attached to the aromatic ring (like aryl methyl groups) typically appear as singlets because they are deshielded and don't have neighboring protons. However, if the methyl groups are part of a larger substituent, like an ester group (O-C-O), then the methyl might be next to an oxygen, but in that case, the methyl would be split. Wait, but the NMR shows two signals for CH3. If they are singlets, maybe each methyl is attached to the ring as a single substituent. Alternatively, if there are two methyl groups, each as singlets, then that would account for two CH3 signals. But the question mentions a di-substituted ring, so there are two substituents on the ring. If one of the substituents is an ester group (O-CO-O), then the other substituent could be a methyl group. Wait, but an ester group would be OOCR, so the substituent would be -OOCR. But in that case, the methyl group from the ester would be attached to the oxygen. Let me think. If the substituent is an ester, like -OOCR, then the structure would be Ar-O-CO-O-R, but that's not typical. Wait, no. Ester groups are typically R-O-CO-R'. So the substituent would be -O-CO-O-R, but that's not possible. Wait, no, esters are R-O-CO-R', where R is an alkyl or aryl group. So the substituent on the benzene ring would be -O-CO-R, where R is an alkyl group. For example, an ester group would be like -O-CO-CH3 (methyl ester) or -O-CO-CH2CH3 (ethyl ester), etc. But in the NMR, the –CH3 groups are present. Wait, but if the substituent is an ester group, the oxygen is directly attached to the benzene ring. So the structure would be benzene with a substituent -O-CO-R. Then, the R group would be another substituent. Alternatively, maybe the substituent is an ester group like -O-CO-CH2-... but then there might be multiple CH2 groups, but the problem states there are no signals for CH2 groups. So perhaps the substituent is a methyl ester, like -O-CO-CH3. Then the methyl group (CH3) attached to the oxygen would be a singlet in the NMR. However, the problem states that there are two CH3 signals. So maybe there are two methyl groups attached elsewhere. Wait, but if the substituent is an ester group, maybe the aromatic ring has two substituents: one ester group (like -O-CO-CH3) and another group, perhaps a methyl group attached directly to the ring. But then the NMR would show two CH3 signals: one from the ester and one from the methyl group. But in that case, the NMR would have two CH3 signals. However, the problem states that the compound is di-substituted, so two substituents on the ring. If one substituent is the ester group (-O-CO-CH3) and the other is a methyl group (-CH3), then the NMR would have two CH3 signals. But the problem says "no signals corresponding to CH2 groups," so that seems possible.

Wait, but let's think again. If the substituent is an ester group, like -O-CO-CH3, then the structure would be benzene-O-CO-CH3. But then the benzene ring would have only one substituent, but the problem says it's di-substituted. So there must be two substituents. Therefore, the substituents could be -O-CO-CH3 and another substituent. Alternatively, maybe the substituent is a benzene ring with two ester groups, but that would complicate the NMR.

Alternatively, perhaps the substituents are a benzene ring with an ester group (like -O-CO-CH3) and a methyl group attached directly to the ring (Ar-CH3). Then the substituents would be the ester and the methyl group, making it di-substituted. That would account for two substituents. Then the NMR would show two CH3 signals: one from the ester (as a singlet, since it's attached to oxygen) and one from the methyl group attached to the ring (also a singlet). But wait, the NMR shows two CH3 signals in total. So if there are two substituents, each contributing a methyl group, that would make sense. For example, if the substituents are -O-CO-CH3 and -CH3, then you have two CH3 groups. But the problem states that the substituents are di-substituted, so two substituents on the ring. So each substituent could have a methyl group. But then the substituent groups themselves would have methyl groups. For example, one substituent is a methyl ester (-O-CO-CH3) and another substituent is a methyl group (-CH3). But then the aromatic ring is di-substituted with two substituents, each possibly contributing a methyl group. However, the problem states the substituents are di-substituted, so maybe each substituent is a different group. Wait, perhaps one substituent is a methyl ester (-O-CO-CH3) and the other substituent is a methyl group (-CH2-...? No, because the NMR shows no CH2 groups. Hmm.

Wait, maybe I'm overcomplicating. Let's try to approach this step by step.

First, the FTIR shows an ester group. So the functional group is an ester. The molecular formula would include the ester group, which is O-CO-O. Wait, no. An ester has the structure R-O-CO-R'. So the formula would include an oxygen from the oxygen in the ether linkage and two oxygens from the carbonyl. Wait, no. Wait, the ester functional group is R-O-CO-R', where R and R' are alkyl or aryl groups. So the formula would have two oxygens in the ester group. But in the molecular formula of the compound, we need to account for all the oxygens. The molecular formula options are C11H12O2, C11H14O2, C12H12O2, C12H14O2. So the ester group accounts for two oxygens.

Now, the NMR shows six signals:

- Two aromatic-H: this suggests that the aromatic ring has two distinct types of protons. For example, in a para-substituted benzene ring with two different substituents, you might get two sets of aromatic protons. But since it's di-substituted, maybe the substituents are in positions that create two sets of equivalent protons. For example, if the substituents are meta and para to each other, but that might complicate things. Alternatively, if the substituents are in positions that split the ring into two sets of equivalent protons. For instance, if the substituents are para to each other, then the ring would have two sets of equivalent protons (ortho and meta). Wait, no. If you have two substituents para to each other, the ring would have two sets of equivalent protons: the two protons adjacent to one substituent (ortho) and the two protons adjacent to the other substituent (ortho to the other substituent), but wait, if substituents are para, then the two substituents are across from each other. So the ring would have two sets of equivalent protons: the two ortho to substituent A and the two ortho to substituent B. But substituent A and B are para, so the ring would have two sets of two equivalent protons each. But the NMR shows two signals for aromatic-H, which could mean four aromatic protons. Wait, but a benzene ring has six protons. If it's di-substituted, the number of aromatic protons depends on the substitution pattern. For example, para substitution would leave four equivalent protons (each pair ortho to the substituents), but wait, no. Let me think. If the substituents are in the para positions, then the two substituents are across from each other. The ring would have four equivalent protons (two ortho to substituent A and two ortho to substituent B), but these two sets of two protons each would not be equivalent because the substituents are different. Wait, but if the substituents are the same, then the four protons would be split into two sets of two, but if the substituents are different, then the four protons would be split into two sets of two non-equivalent protons. However, in this case, the substituents are an ester group and a methyl group. So the substituents are different. Therefore, the four aromatic protons would split into two sets of two, each set being non-equivalent. But the NMR shows two signals for aromatic-H, which would correspond to two sets of equivalent protons. Wait, but if there are four aromatic protons in two sets of two, that would result in two signals. So that's possible. For example, if the substituents are in the para positions, each substituent causing two sets of equivalent protons. So the aromatic ring would have two sets of two equivalent protons each, leading to two signals in the NMR. That makes sense.

Next, the vinyl-H signals: two signals, one doublet and one doublet of quartets. Vinyl protons are typically adjacent to a double bond. If the structure has a vinyl group (like CH2=CH-), the protons on the CH2 would split into a doublet if each is next to a single proton (like a CH group), or a quartet if each is next to two protons (like a CH2 group). Wait, but the problem states that there are no signals corresponding to CH2 groups. So the CH2 groups are not present. Therefore, the vinyl protons must be in a position where they are adjacent to a CH group, leading to coupling. For example, if there is a structure like CH2=CH-O-R, then the two protons on the CH2 would each couple with the CH group, leading to a doublet. But the problem states no CH2 groups, so maybe the substituents are not CH2 but rather something else. Alternatively, if the substituent is a vinyl group attached to another group, like a conjugated system. For example, if the substituent is a vinyl group (CH2=CH-) attached to an oxygen (like O-CH2-CH2-... but that would introduce CH2 groups, which are not present). Alternatively, maybe the substituent is a group like CH2=CH-O-CO-CH3 (the ester group). Then the vinyl protons (CH2=CH-) would be adjacent to the oxygen. But then the protons on the CH2 would be split by the adjacent protons. Wait, in that case, the CH2 group would be split by the adjacent CH group. For example, if the substituent is CH2=CH-O-R, then the CH2 protons would couple with the adjacent CH group, leading to a doublet of quartets. But the problem says there are no CH2 groups. Wait, the problem says "no signals corresponding to –CH2 groups." So the substituent cannot have a CH2 group. Therefore, the substituent must be a group without CH2. So the substituent must be something like CH2=CH-O-R, but that would have CH2 groups. Hmm, this is confusing. Alternatively, perhaps the substituent is a group like CH2=CH-CO-O-R, but again, that would involve a CH2 group. Alternatively, maybe the substituent is a group like CH2=CH-O-CO-CH3, but that would have a CH2 group. Wait, but the problem states there are no CH2 groups, so that can't be. Therefore, perhaps the substituent is a group like CH2=CH-CO-O-R, but that would have a CH2 group. So maybe the substituent is not a CH2 group but something else. Wait, maybe the substituent is a group like CH2=CH-CO-O-R, but then the CH2 group is present, which is not allowed. Therefore, maybe the substituent is a group like CH2=CH-CO-O-R, but the problem says no CH2 groups. So this seems contradictory. Alternatively, perhaps the substituent is a group where the CH2 is not present. Wait, maybe the substituent is a group like CH2=CH-O-CO-CH3, but that would have a CH2 group. Hmm. Maybe the substituent is a group like CH2=CH-O-R where R is a group without CH2. Wait, but if R is an ester group, then R would be O-CO-CH3. So the substituent would be CH2=CH-O-CO-CH3. But then the CH2 group is present, which is not allowed. Therefore, this seems impossible. Maybe I'm missing something here. Let's think differently. The vinyl protons are two signals: one is a doublet, the other is a doublet of quartets. Since there are no CH2 groups, perhaps the substituent is a group where the two protons are each next to a single proton. For example, if the substituent is a group like CH2=CH-CO-O-R, but then the CH2 group is present. Alternatively, maybe the substituent is a group like CH=CH-CO-O-R. Wait, but that's not a vinyl group. Wait, vinyl groups are CH2=CH-... but if the substituent is CH=CH-..., that's an allene, which is different. But I'm not sure. Alternatively, maybe the substituent is a group like O-CO-CH2-CH2-..., but that would have CH2 groups. Hmm. This is confusing. Let me think again. The NMR shows two signals for vinyl-H: one doublet and one doublet of quartets. Since there are no CH2 groups, the substituent must be such that the protons are adjacent to a single proton. For example, if the substituent is a group like CH2=CH-X, where X is a single proton. But then the CH2 group would have two protons, each coupling with the adjacent proton (X), leading to a doublet of doublets. But the problem states there are no CH2 groups. Therefore, perhaps the substituent is a group where the two protons are each adjacent to a single proton. For example, if the substituent is a group like CH2=CH-CO-O-R, but again, that would have a CH2 group. Alternatively, maybe the substituent is a group like CH2=CH-CO-O-R, but R is a group without CH2. Wait, but R would be part of the ester group. Let me think. If the substituent is an ester group, like -O-CO-CH3, then the benzene ring has substituents -O-CO-CH3 and another substituent, perhaps a methyl group. But then the substituents would be -O-CO-CH3 and -CH3. So the aromatic ring would have substituents in positions that create two distinct aromatic protons. Then the vinyl protons would be part of the ester group. Wait, but the ester group is an oxygen connected to a carbonyl and a methyl group. So the structure would be Ph-O-CO-CH3. But that's a single substituent, not di-substituted. Therefore, the di-substituted ring must have two substituents: one ester group and another group. The other group could be a methyl group. So the structure would be Ph-O-CO-CH3 and Ph-CH3. But wait, that would make the ring di-substituted with two substituents: one ester group and one methyl group. Then the aromatic protons would be in two different environments, leading to two signals. The ester group would contribute no protons, as it's O-CO-CH3. The methyl group would contribute a singlet. But wait, the NMR shows two CH3 signals. So if there are two substituents, each contributing a CH3 group, that would account for two CH3 signals. For example, one substituent is -O-CO-CH3 and the other is -CH3. Then the aromatic ring would have two substituents: one ester group and one methyl group. The aromatic protons would be split into two signals, as explained earlier. The ester group contributes a CH3 (singlet), and the methyl group contributes another CH3 (singlet). So that would explain two CH3 signals. The vinyl protons would be from the ester group's structure. Wait, but the ester group is -O-CO-CH3, which doesn't have any protons. Therefore, the vinyl protons must be from a different substituent. Hmm, this is confusing. Maybe the substituent is not an ester but an ester group attached to the benzene ring. Wait, but the FTIR shows an ester group, so the substituent must have an ester. Alternatively, perhaps the substituent is a group like CH2=CH-O-CO-CH3. But then the CH2 group would be present, which is not allowed. Therefore, perhaps the substituent is a group like CH2=CH-O-CO-CH3, but the problem states there are no CH2 groups. Therefore, this seems impossible. Maybe the substituent is a group like CH2=CH-O-CO-CH2-... but that would introduce CH2 groups. Hmm.

Alternatively, perhaps the substituent is a group like CH2=CH-CO-O-R, but again, the CH2 group is present. Wait, but the problem states there are no CH2 groups. Therefore, this approach is not working. Let me think differently. Maybe the substituent is a group where the protons are not adjacent to any CH2 groups. For example, if the substituent is a group like CH2=CH-CH2-CO-O-R, but again, that would have CH2 groups. Alternatively, maybe the substituent is a group like CH2=CH-CO-O-R, but then the CH2 group is present. Hmm. This is a bit of a dead end. Let me try to approach this from another angle.

The molecular formula is either C11H12O2, C11H14O2, C12H12O2, or C12H14O2. Let's calculate the degree of unsaturation to get more information.

Degree of unsaturation (DoU) is calculated as DoU = (2C + 2 - H - X + N)/2. Assuming no halogens or nitrogen, DoU = (2*6 + 2 - 6 - 0)/2 = (14 -6)/2 = 8/2 = 4. So four degrees of unsaturation. For a benzene ring (which has three degrees of unsaturation: three double bonds in the ring), and one double bond (from the ester group). Wait, the ester group has a double bond between the carbonyl and the oxygen. So that's one double bond. The benzene ring has three degrees (three double bonds). So total so far: 4. Therefore, the molecule has a benzene ring (3 DoU) and one double bond (1 DoU) from the ester group. That adds up to 4. So the rest of the structure must be saturated. Therefore, the molecule has a benzene ring and a double bond (from the ester), and the rest is single bonds.

So the structure is a di-substituted benzene ring with an ester group and another substituent. The substituents are -O-CO-CH3 and -CH3. Wait, but then the ester group would be part of the substituent. Let me think again. The substituents on the benzene ring are -O-CO-CH3 and -CH3. The ester group would be O-CO-CH3, which is attached to the benzene ring. Then the benzene ring has substituents at two positions, say para to each other. Then the aromatic protons would be split into two sets. The ester group contributes a CH3 (singlet), and the methyl group contributes another CH3 (singlet), so two CH3 signals. The ester group doesn't have any protons. The vinyl protons would come from a double bond. Wait, but how? If the substituent is an ester group, there's no double bond. The double bond would be in the benzene ring (if substituted at two positions, the ring would have a double bond, but benzene rings are already fully conjugated). Wait, no. The benzene ring is a six-membered ring with alternating double bonds. So if the substituents are in the para positions, the ring would still have three double bonds. Therefore, the double bond in the ester group is a separate double bond. Wait, no. The ester group is O-CO-CH3, which is a single substituent. So the double bond is in the ester group? No, the ester group is O-CO-R. The carbonyl is a double bond between the oxygen and the carbon. So the ester group does have a double bond. Therefore, the molecule has a benzene ring (3 DoU) and the ester group (1 DoU), totaling 4 DoU. That matches the degree of unsaturation.

So the structure is a benzene ring with two substituents: one ester group (-O-CO-CH3) and another methyl group (-CH3). The ester group contributes the two oxygens (O-CO-CH3 has two O's), and the methyl group contributes one O (from the ester's oxygen). Wait, but the ester group is O-CO-CH3, so that's two O's in the ester. The benzene ring has no O's. So the total O's in the molecule are two (from the ester group). The molecular formula would be CnHmO2. Let's check the options:

A. C12H14O2
B. C11H12O2
C. C12H12O2
D. C11H14O2

So the O's are accounted for in all options. Now, the carbons: the benzene ring has six carbons. The ester group is O-CO-CH3: that's one O, one C (the carbonyl C), and one CH3 (another C). Wait, no. The ester group is O-CO-CH3. So the carbonyl C is part of the ester. So the substituent is O-CO-CH3: that's three carbons (O is not a carbon). Wait, no. The substituent is -O-CO-CH3. The carbonyl is part of the ester. So the substituent is a methoxycarbonyl group: O-CO-CH3. So the substituent contributes three carbons: the O is not a carbon, the carbonyl C is one carbon, and the CH3 is another. Wait, but O-CO-CH3 is -O-C(O)-CH3. So the substituent is three carbons: O (not a C), C (from CO), and CH3 (another C). Wait, no. Wait, the substituent is O-CO-CH3. The carbonyl is C=O. So the substituent is O-C(O)-CH3. Therefore, the substituent has two carbons: the carbonyl C and the CH3's C. Wait, no. Wait, the substituent is O-CO-CH3. The structure is O-C(=O)-CH3. So the substituent has three atoms: O, C (from CO), and CH3. But the substituent's carbon count: the carbonyl is one C, and the CH3 is another C. So the substituent contributes two carbons. The benzene ring has six carbons. The substituents are the ester group (two carbons) and the methyl group (one carbon). So total carbons: 6 (ring) + 2 (ester) + 1 (methyl) = 9? But the options are C11, C12, etc. Wait, that can't be right. Wait, maybe I'm miscalculating. Let me think again. The benzene ring has six carbons. The substituent is an ester group (-O-CO-CH3), which is two carbons (the CO and the CH3). The other substituent is a methyl group (-CH3), which is one carbon. So total carbons: 6 + 2 + 1 = 9. But the options have 11 or 12 carbons. Therefore, this suggests that my initial assumption is incorrect. Therefore, there must be more carbons in the substituents.

Wait, maybe the substituent is not just the ester group. If the substituent is a longer chain, perhaps. For example, if the substituent is an ester group with a longer chain. Wait, but the problem states it's a di-substituted aromatic ring, so two substituents on the ring. If one substituent is an ester group, and the other is a methyl group, then the total carbons would be 6 (ring) + 2 (ester) + 1 (methyl) = 9. But the options have 11 or 12. Therefore, this approach is not working. Maybe the substituent is not just the ester group but includes other groups. Wait, perhaps the substituent is an ethyl ester. For example, -O-CO-CH2CH3. But then the substituent would be three carbons (the CO and the CH2CH3), but then the NMR would show more protons. Also, the problem states there are no CH2 groups, so the substituent cannot have CH2. Therefore, the substituent must be a methyl ester, -O-CO-CH3. But then the total carbons are 9, which doesn't match the options. Therefore, I must be missing something.

Wait, perhaps the substituent is a group where the ester is connected to a chain that includes more carbons. For example, if the substituent is a group like -O-CO-CH2-C(...), but that would introduce CH2 groups, which are not allowed. Alternatively, maybe the substituent is part of a longer chain. Wait, but the problem says it's di-substituted, so two substituents on the ring. Therefore, the substituents must be such that the total carbons add up to 11 or 12. Let's think again.

Each substituent contributes carbons. The benzene ring is 6 C. The ester group is O-CO-CH3: that's two C (CO and CH3). The other substituent is a methyl group (-CH3): one C. So total so far: 6 + 2 + 1 = 9. To reach 11 or 12, there must be more carbons in the substituents. Therefore, perhaps the substituent is not just the ester group but includes another group. Wait, but the substituent is part of the ester. Wait, maybe the substituent is a group like -O-CO-CH2-C..., but that would introduce CH2 groups, which are not allowed. Alternatively, perhaps the substituent is a group like -O-CO-CH(CH3)2 or something else. Wait, but then there would be CH2 groups. Hmm. Alternatively, maybe the substituent is a group like -O-CO-CH2-CO-O-R, but that's getting too complex. Alternatively, perhaps the substituent is a group like -O-CO-CH2-CH2-O-R, but that would have CH2 groups. I'm stuck here. Let me think differently.

Wait, the problem states the compound is di-substituted. So two substituents on the benzene ring. Each substituent can be a group with multiple carbons. For example, one substituent is -O-CO-CH2CH2CH2... but that would have CH2 groups. Alternatively, perhaps the substituent is a group like -O-CO-CH(CH2CH3)2, but that would have CH2 groups. Hmm. Alternatively, maybe the substituent is a group like -O-CO-CH3 and another substituent like -CH2CH2CH2CH3, but that would have CH2 groups. Wait, but the problem states there are no CH2 groups. Therefore, the substituents must not have any CH2 groups. Therefore, the substituents must be either -O-CO-CH3 or -CH3. But then the total carbons would be 9, which doesn't match the options. Therefore, this suggests that the substituent is not just the ester group but includes another group. Wait, but how?

Alternatively, perhaps the substituent is part of a longer chain. For example, if the substituent is -O-CO-CH2-CO-O-R, but that would have CH2 groups. Alternatively, maybe the substituent is a group like -O-CO-CH2-CH2-O-CO-R, but again, CH2 groups. This seems impossible. Therefore, perhaps the substituent is not part of the ester group but is a separate group. Wait, but the FTIR shows an ester group, so the substituent must be part of the ester. Therefore, I must be missing something.

Wait, let's consider the molecular formula options. Let's take option D: C11H14O2. Total carbons: 11. Benzene ring: 6. Therefore, substituents contribute 5 carbons. If one substituent is -O-CO-CH3 (3 carbons) and the other is -CH2CH2CH3 (3 carbons), but that would have CH2 groups. Alternatively, if substituent 1 is -O-CO-CH3 (3 carbons) and substituent 2 is -CH3 (1 carbon), total 4, but the options have 11. Therefore, this approach is not working. Let me check the options again.

Wait, maybe the substituent is a group like -O-CO-CH2-CH2-O-R, but again, that would have CH2 groups. Alternatively, perhaps the substituent is part of a larger molecule. Wait, maybe the substituent is a group like -O-CO-CH2-CH2-O-CO-R, but that's getting too complex. Alternatively, maybe the substituent is a group like -O-CO-CH3 and another substituent like -CH2CH2CH2CH3, but that would have CH2 groups. Therefore, this approach is not working. I must be missing something here.

Wait, perhaps the substituent is a group like -O-CO-CH2-CO-O-R, but that would introduce a carbonyl group and a CH2 group. But the problem states there are no CH2 groups. Therefore, this is impossible. Therefore, perhaps the substituent is not part of the ester group but is a separate group. Wait, but the FTIR shows an ester group, so the substituent must be part of the ester. Therefore, I'm stuck here. Let me try to think differently.

Let me consider the molecular formula options. Let's take option B: C11H12O2. Total carbons: 11. Benzene ring: 6. Therefore, substituents contribute 5. If substituent 1 is -O-CO-CH3 (3 carbons) and substituent 2 is -CH2CH2CH3 (3 carbons), but that would have CH2 groups. Alternatively, substituent 2 is -CH3 (1 carbon), and substituent 1 is -O-CO-CH2CH2CH3 (4 carbons), but that would have CH2 groups. Therefore, this is impossible. Therefore, the substituents must be such that they don't have CH2 groups. Therefore, the substituents must be -O-CO-CH3 and -CH3. That gives 3 + 1 = 4 carbons, but the options have 11 or 12. Therefore, this approach is not working. Therefore, perhaps the substituent is not just the ester group but includes another group. Wait, but how?

Wait, perhaps the substituent is a group like -O-CO-CH2-CH2-... but that would have CH2 groups. Alternatively, perhaps the substituent is a group like -O-CO-CH2-CH2-O-R, but again, CH2 groups. Therefore, this seems impossible. Therefore, I must have made a mistake in my earlier assumption. Let me go back.

Wait, the problem states the compound is di-substituted. Therefore, there are two substituents on the benzene ring. The substituents must be such that the total carbons in the substituents plus the ring equals the molecular formula. Let's take option D: C11H14O2. Benzene ring: 6 C. Substituents: 5 C. If substituent 1 is -O-CO-CH3 (3 C) and substituent 2 is -CH2CH2CH3 (3 C), but that's 6 C, which is too much. Alternatively, substituent 1 is -O-CO-CH3 (3 C) and substituent 2 is -CH3 (1 C), total 4 C. That's not enough. Therefore, this option can't be correct. Similarly, option C: C12H12O2. Substituents contribute 6 C. If substituent 1 is -O-CO-CH3 (3 C) and substituent 2 is -CH2CH2CH2CH3 (4 C), but that would have CH2 groups. Therefore, this is impossible. Therefore, perhaps the substituents are -O-CO-CH2-CH2-... but again, CH2 groups are present. Therefore, this approach is not working.

Wait, perhaps the substituent is a group like -O-CO-CH2-CH2-O-R, but that would have CH2 groups. Therefore, this is impossible. Therefore, I must be missing something here. Let me think differently.

Perhaps the substituent is part of a longer chain. For example, the substituent is -O-CO-CH2-CH2-CO-O-R, but that would have CH2 groups. Alternatively, perhaps the substituent is a group like -O-CO-CH2-CO-O-R, but that would have a carbonyl group. Wait, but that would still have CH2 groups. Therefore, this seems impossible. Therefore, I must conclude that the substituent is not part of the ester but is a separate group. But the FTIR shows an ester group, so this is impossible.

At this point, I'm stuck. Let me try to summarize what I have so far:

- The compound is di-substituted aromatic (benzene ring with two substituents).
- FTIR shows ester group (O-CO-), so there's an ester substituent.
- NMR shows two aromatic protons (two signals), two vinyl protons (doublet and doublet of quartets), two CH3 signals.
- No signals for –CH2 groups.
- Molecular formula options are C11H12O2, C11H14O2, etc.

Given that, the structure must have a benzene ring with two substituents: one ester group and another group with two CH3 protons. The ester group contributes the O-CO-CH3 (so one CH3), and the other substituent must contribute another CH3. Therefore, the substituents are -O-CO-CH3 and -CH3. The benzene ring is six carbons. The ester substituent is three carbons (O-CO-CH3), and the methyl substituent is one carbon. Therefore, total carbons: 6 + 3 + 1 = 10. But the options are 11 or 12. Therefore, there's a discrepancy here. Therefore, perhaps the substituent is not just the ester group but includes another group. For example, if the substituent is a longer chain. But then the NMR would show more protons. Alternatively, perhaps the substituent is a group like -O-CO-CH2-CH2-..., but that would introduce CH2 groups, which are not allowed. Therefore, this seems impossible.

Alternatively, perhaps the substituent is a group like -O-CO-CH(CH3)2. That would have a CH group and two CH3 groups. But then the NMR would show a CH signal, which is not present. The problem states there are no signals corresponding to –CH2 groups, but there are CH groups? Wait, the problem states "no signals corresponding to –CH2 groups". CH groups would give singlets or other signals, but they are not –CH2 groups. Therefore, that's allowed. However, the substituent would have a CH group, which would give a signal. But the NMR shows only CH3 signals. Therefore, that's not possible. Therefore, the substituent cannot have any CH groups. Therefore, the substituent must be -O-CO-CH3 and another group that doesn't have CH groups. The only group that fits is -CH3. Therefore, the substituents are -O-CO-CH3 and -CH3. Total carbons: 6 (ring) + 3 (ester) + 1 (methyl) = 10. But the options are 11 or 12. Therefore, there's a problem here.

Wait, maybe the substituent is not only the ester group but includes another oxygen. For example, if the substituent is -O-CO-CH3 and another substituent is -OCH3. But then the NMR would show a CH3 from the ester (singlet) and a CH3 from the ether group (singlet). That would match the two CH3 signals. The aromatic protons would be as before. The vinyl protons would be from the ester's structure. But the ester group is O-CO-CH3, which doesn't have any protons. Therefore, the vinyl protons must be from another part. Wait, but if the substituent is -O-CO-CH3 and -OCH3, then the aromatic ring would have substituents in the para positions, leading to two sets of aromatic protons. The NMR would show two aromatic signals. The ester and ether substituents would contribute two CH3 signals. The vinyl protons would be none, because the ester group doesn't have any. Therefore, this does not match the FTIR data, which shows an ester group. Therefore, this approach is incorrect.

I'm stuck. Given the time I've spent, perhaps it's best to look for another approach. Let's consider the molecular formula options and the substituents. The substituents must account for the molecular formula difference from the benzene ring. Benzene is C6H6. The options are C11H12O2, C11H14O2, C12H12O2, C12H14O2. The difference from C6H6 is:

For C11H12O2: 11-6 = 5 C, 12-6 = 6 H, 2 O.

For C12H14O2: 12-6 = 6 C, 14-6 = 8 H, 2 O.

So the substituents must contribute 5 or 6 carbons and 6 or 8 hydrogens, along with 2 oxygens. The oxygens come from the ester group (O-CO-CH3), which contributes two oxygens. Therefore, the substituents must not contribute any additional oxygens. Therefore, the other substituent must be a methyl group (-CH3), which contributes one carbon and three hydrogens. Therefore, the substituents are -O-CO-CH3 (3 carbons) and -CH3 (1 carbon). Total substituent carbons: 4. Benzene ring: 6. Total: 10. But the options have 11 or 12. Therefore, this is impossible. Therefore, there must be another substituent. Wait, but the problem states it's di-substituted, so two substituents. Therefore, perhaps the substituents are -O-CO-CH2-CH2- and -CH3. But that would have CH2 groups. Therefore, this is impossible. Therefore, I must conclude that the substituents are -O-CO-CH3 and -CH3, contributing 4 carbons, but the options require 5 or 6 more carbons. Therefore, this is impossible. Therefore, perhaps the correct answer is not among the options, but that's unlikely. Therefore, I must have made a mistake in my earlier reasoning.

Wait, perhaps the substituent is not just the ester group but includes another group. For example, if the substituent is -O-CO-CH2-C(O)O-R, but that would have a carbonyl group and a CH2 group. Therefore, the NMR would show more signals, which is not the case. Therefore, this is impossible.

At this point, I think I need to consider that the substituent is a group like -O-CO-CH2-CH2-O-R, but that would have CH2 groups. Therefore, this is impossible. Therefore, the only possible structure is a benzene ring with two substituents: one ester group (-O-CO-CH3) and another methyl group (-CH3). The total carbons would be 6 (ring) + 3 (ester) + 1 (methyl) = 10. But the options are 11 or 12. Therefore, there's a discrepancy here. Therefore, perhaps the substituent is not just the ester group but includes another group. For example, if the substituent is -O-CO-CH2-CH2-O-R, but that would have CH2 groups. Therefore, this is impossible.

Given that, I think the correct answer must be option D: C11H14O2. But I can't reconcile the carbons. Alternatively, perhaps the substituent is -O-CO-CH2-CH2-C(O)O-R, but that would have carbonyl groups and CH2 groups. Therefore, this is impossible. Therefore, I think the correct answer is option D: C11H14O2.
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